Steve Bruce's men lie in 11th position, four points shy of the play-off placings, after a superb 12-match unbeaten run.
And Palmer, a first-team regular under Bruce, believes things will become a lot clearer at the top end of the Championship after the next two round of fixtures.
Wednesday are putting the finishing touches to their preparations ahead of a Hillsborough double-header with promotion rivals Aston Villa and Nottingham Forest.
Palmer, a graduate of the Owls' youth system, told The Star: "I definitely think you will have more of an indication after next week (on the promotion race).
"We will look at the table again after the Forest game. Hopefully we will still be in and around the play-offs going into the last five games.
"There are still a lot of points to play for and we will give it a good go."
There are plenty of reasons for Wednesday to be optimistic going into their clash with sixth-placed Villa. You have to go back to November 24 for the last time the Owls lost in their own backyard.
"We know what we are about at Hillsborough," said Scotland international. "We are difficult to beat at home and, fingers crossed, we will pick up some good results."
After taking on Villa and Forest, Bruce's men face daunting trips to automatic promotion hopefuls Norwich City and Leeds United.
Palmer, out of contract at the end of the season, said: "With the teams that we have got left to play, it is there for us. We have got teams to play in and around us. They all have to play each other as well.
"We have given ourselves a fighting chance."